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A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
The generator matrix. The Reed–Muller RM(r, m) code of order r and length N = 2 m is the code generated by v 0 and the wedge products of up to r of the v i, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the
ISO 3166-1 ( Codes for the representation of names of countries and their subdivisions – Part 1: Country codes) is a standard defining codes for the names of countries, dependent territories, and special areas of geographical interest. It is the first part of the ISO 3166 standard published by the International Organization for Standardization .
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations.
A list of the top-level domains by the Internet Assigned Numbers Authority (IANA) is maintained at the Root Zone Database. [1] IANA also oversees the approval process for new proposed top-level domains for ICANN. As of April 2021 [update], their root domain contains 1502 top-level domains. [2] [3] As of March 2021 [update], the IANA root ...
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix . This is a matrix such that Had ( x ) = x ⋅ G {\displaystyle {\text{Had}}(x)=x\cdot G} holds for all x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} , where the message x {\displaystyle x} is viewed as a row vector and the vector-matrix product ...
A generator matrix for the binary Golay code is I A, where I is the 12×12 identity matrix, and A is the complement of the adjacency matrix of the icosahedron. A convenient representation. It is convenient to use the "Miracle Octad Generator" format, with co-ordinates in an array of 4 rows, 6 columns. Addition is taking the symmetric difference.
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